Warm Up Solutions

Simplify.

Note

Problems 1–2
Q: What must be determined before adding and subtracting fractions?
A: The least common denominator (LCD)

Using the LCD rather than the Rule of Four will be more efficient when working with rational expressions.

$LCD (5, 3) = 15 \frac{9}{15} - \frac{25}{15} - \frac{16}{15}$

$LCD (4, 2, 10) = 20 \frac{5 x}{20} + \frac{40 x}{20} - \frac{2 x}{20} \frac{43 x}{20}$

$(\frac{2}{2} + \frac{1}{2}) \div 10 \frac{3}{2} \cdot \frac{1}{10}$

$\frac{3}{20}$

$\frac{5}{8} \div \frac{15}{16} \frac{{}^{1}5}{{}_{1}8} \cdot \frac{16^{2}}{15_{3}}$

Note

Simplify before multiplication.

$\frac{2}{3}$

Note

Q: What math operation does the fraction bar represent?
A: Division

Recall that dividing by a fraction is the same as multiplying by its reciprocal.